Holyrood Mathematics Department Numeracy across the curriculum Parent and Pupil Numeracy support booklet - Holyrood Secondary School

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Holyrood Mathematics Department Numeracy across the curriculum Parent and Pupil Numeracy support booklet - Holyrood Secondary School
Parent and Pupil Numeracy Booklet

 Holyrood
 Mathematics
 Department

 Numeracy across
 the curriculum

 Parent and Pupil
 Numeracy support
 booklet
Holyrood Mathematics Department Numeracy across the curriculum Parent and Pupil Numeracy support booklet - Holyrood Secondary School
Parent and Pupil Numeracy Booklet

Introduction

This information booklet has been produced as a guide for parents and pupils to make you
more aware of how each topic is taught within the Mathematics and Numeracy
department at Holyrood Secondary School.

We understand mathematics can be daunting for some parents and we hope that the
information in this booklet will lead to a more consistent approach to the learning and
teaching of Numeracy topics across the curriculum which will hopefully help you at home.

We have used specific terminology and methodologies that we believe is best for each
topic taught in our school. To help you understand better, we have included a glossary of
common maths terminology as well as worked examples with pictorial representations for
each topic.

If you would like further examples, explanations and the opportunity to try some
yourself, there are videos available by clicking the links associated with each topic.

We as teachers do not expect pupils to get every single question correct for homework or classwork.
In fact, getting things wrong is part of learning. We encourage you to allow your child to work alone
and to only help when they are stuck, referring to this document should you need it.

We hope that this document, in addition to your support and your child’s persistent effort, will lead to
an improvement in progress/attainment and confidence for all pupils.

Many thanks for your continued support

Holyrood Mathematics Department
Holyrood Mathematics Department Numeracy across the curriculum Parent and Pupil Numeracy support booklet - Holyrood Secondary School
Parent and Pupil Numeracy Booklet

 Mathematical Dictionary (Key Words)

 Add; Addition (+) To combine two or more numbers to get one number
 (called the sum or the total)
 e.g. 23 + 34 = 57
 a.m. (ante meridiem) Any time in the morning (between
 midnight and 12 noon).
 Approximate An estimated answer, often obtained by rounding to
 the nearest 10, 100, 1000 or decimal place.
 Calculate Find the answer to a problem (this does not mean
 that you must use a calculator!).
 Data A collection of information (may include facts,
 numbers or measurements).
 Denominator The bottom number in a fraction (the number of
 parts into which the whole is split).
 Difference (-) The amount between two numbers (subtraction).
 e.g. the difference between 18 and 7 is 11
 18 – 7 = 11
 Division (÷) Sharing into equal parts
 e.g. 24 ÷ 6 = 4
 Double Multiply by 2.
 Equals (=) The same amount as.
 Equivalent Fractions which have the same vale
 fractions 4 1
 e.g. and are equivalent fractions.
 8 2
 Estimate To make an approximate or rough answer, often by
 rounding.
 Evaluate To work out the answer/find the value of.
 Even A number that is divisible by 2.
 Even numbers end in 0, 2, 4, 6, or 8.
 Factor A number which divides exactly into another number,
 leaving no remainder.
 e.g. The factors of 15 are 1, 3, 5 and 15.
 Frequency How often something happens. In a set of data, the
 number of times a number or category occurs.
 Greater than (>) Is bigger or more than
 e.g. 10 is greater than 6 i.e. 10 > 6
 Greater than or Is bigger than OR equal to.
 equal to (>)
 Least The lowest (minimum).
Holyrood Mathematics Department Numeracy across the curriculum Parent and Pupil Numeracy support booklet - Holyrood Secondary School
Parent and Pupil Numeracy Booklet

 Less than (
Holyrood Mathematics Department Numeracy across the curriculum Parent and Pupil Numeracy support booklet - Holyrood Secondary School
Quadrilateral A polygon with 4 sides.
 Quotient The number resulting by dividing one number by
 another
 e.g. 20 ÷ 10 = 2, the quotient is 2.
 Remainder The amount left over when dividing a number by one
 which is not a factor.
 Share To divide into equal groups.
 Sum The total of a group of numbers (found by adding).
 Square Numbers A number that results from multiplying a number by
 itself
 e.g. 6² = 6  6 = 36.
 Total The sum of a group of numbers (found by adding).

 Addition (+) Subtraction (-)
 • sum of • less than
 • more than • take away
 • add • minus
 • total • subtract
 • and • difference
 • plus between
 • increase Equals (=) • reduce
 • altogether • is equal to • decrease
 • same as
 • makes
 • will be

 Multiplication (×) Division (÷)
 • multiply • divide
 • times • share equally
 • product • split equally
 • of • groups of
 • per

5
Holyrood Mathematics Department Numeracy across the curriculum Parent and Pupil Numeracy support booklet - Holyrood Secondary School
Parent and Pupil Numeracy Booklet

Index

 1. Addition
 2. Subtraction
 3. Multiplication
 4. Division
 5. Rounding
 6. Order of Operations
 7. Integers
 8. Fractions
 9. Percentages
 10. Ratio
 11. Proportion
 12. Time
 13. Bar Graphs
 14. Line graphs
 15. Scatter graphs
 16. Pie Charts
 17. Averages
 18. Evaluating Formulae
 19. Collecting like terms

 6
Holyrood Mathematics Department Numeracy across the curriculum Parent and Pupil Numeracy support booklet - Holyrood Secondary School
Parent and Pupil Numeracy Booklet

Addition https://corbettmaths.com/2013/12/19/addition-
 video-6/

 1. Mental Strategies

 There are a number of useful mental strategies for addition. Some
 examples are given below.

 Example: Calculate 34 + 49

 Method 1 Add the tens, add the units, then add together

 30 + 40 = 70 4 + 9 = 13 70 + 13 = 83

 Method 2 Add the tens of the second number to the first and then
 add the units separately

 34 + 40 = 74 74 + 9 = 83

 Method 3 Round to the nearest ten, then subtract

 34 + 50 = 84 (50 is 1 more than 49 so subtract 1)
 84 – 1 = 83

 2. Written Method

 Before doing a calculation, pupils should be encouraged to make an
 estimate of the answer by rounding the numbers. They should also be
 encouraged to check if their answers are sensible in the context of the
 question.

 Example: 3456 + 975

 3 456 + 975 We add the numbers in
 Line up the
 each column from right
 numbers according Estimate
 3 500 + 1 000 = 4 500 to left
 to place value
 3 4 5 6
 + 1 91 71 5
 4 4 3 1
 Carried numbers are
 written above the line
Holyrood Mathematics Department Numeracy across the curriculum Parent and Pupil Numeracy support booklet - Holyrood Secondary School
Parent and Pupil Numeracy Booklet

Subtraction https://corbettmaths.com/2013/12/19/subtraction-
 video-304/

 1. Mental Strategies

 There are a number of useful mental strategies for subtraction. Some
 examples are given below.

 Example: Calculate 82 – 46

 Method 1 Start at the number you are subtracting and count on

 e.g.

 Method 2 Subtract the tens, then the units

 82 – 40 = 42
 42 – 6 = 36

 2. Written Method

 We use decomposition to perform written subtractions. We “exchange”
 tens for units etc rather than “borrow and pay back”.

 Before doing a calculation, pupils should be encouraged to make an
 estimate of the answer by rounding the numbers. They should also be
 encouraged to check if their answers are sensible in the context of the
 question.

 Example:

 6 286 − 4 857
 We subtract the
 Line up the numbers numbers in each
 Estimate
 according to place 6 300 − 4 900 = 1 400 column from right to
 value left
 5 1 7 1
 6 2 8 6
 − 4 8 5 7
 1 4 2 9
Holyrood Mathematics Department Numeracy across the curriculum Parent and Pupil Numeracy support booklet - Holyrood Secondary School
Parent and Pupil Numeracy Booklet

Multiplication
It is vital that all of the multiplication tables from 1 to 12 are known.
These are shown in the multiplication square below:

  1 2 3 4 5 6 7 8 9 10 11 12
 1 1 2 3 4 5 6 7 8 9 10 11 12

 2 2 4 6 8 10 12 14 16 18 20 22 24
 3 3 6 9 12 15 18 21 24 27 30 33 36
 4 4 8 12 16 20 24 28 32 36 40 44 48

 5 5 10 15 20 25 30 35 40 45 50 55 60
 6 6 12 18 24 30 36 42 48 54 60 66 72
 7 7 14 21 28 35 42 49 56 63 70 77 84
 8 8 16 24 32 40 48 56 64 72 80 88 96
 9 9 18 27 36 45 54 63 72 81 90 99 108
 10 10 20 30 40 50 60 70 80 90 100 110 120

 11 11 22 33 44 55 66 77 88 99 110 121 132

 12 12 24 36 48 60 72 84 96 108 120 132 144

 7 × 8 = 56
Mental Strategies

 Example: Find 39 x 6

 Method 1 Multiply the tens, multiply the units, then add the answers
 together

 30 x 6 = 180 9 x 6 = 54 180 + 24 = 234

 Method 2 Round the number you are multiplying, multiply and then
 subtract the extra

 40 x 6 = 240 (40 is one more than 39 so you
 have multiplied 6 by an extra 1)
 240 – 6 = 234
Parent and Pupil Numeracy Booklet
 https://corbettmaths.com/2013/12/20/multiplicatio
 n-grid-method-video-199/
Grid Method for long multiplication

 Example 1: Calculate 27 × 8
 1. Partition 27 into 20 and 7 × 20 7
 8

 2. Just like the multiplication grid, multiply × then × 
 × 20 7
 8 160 56

 3. Add together 160 and 56
 + = 

 Example 2: Calculate 42 × 35
 1. Partition 42 into 40 and 2 × 40 2
 Partition 35 into 30 and 5 30
 5

 2. Just like above, multiply × , × , × , × 
 × 40 2
 30 1200 60
 5 200 10

 3. Add together all 4 numbers
 + + + = 
Parent and Pupil Numeracy Booklet
 https://corbettmaths.com/2013/02/15/multiplicatio
 n-traditional/
Column Method for long multiplication

 When multiplying by a whole number, pupils should be encouraged to make
 an estimate first. This should help them to decide whether their answer
 is sensible or not.

 Example 357  8
 1 1
 Estimate
 350  2  4 = 700  4 = 2 800

 3 5 7
  8
 The number you are
 4 5

 2 8 5 6
 multiplying by goes
 Carried numbers go under the last digit on
 above the line the right

 Example 329  42
 Multiply by the 2
 Estimate
 Carried numbers 300  40 = 12 000 first from right to
 from multiplication left
 by units go above 3 2 9
 the line
  41 2
 1 63 5 8 Put a zero before
 1 3 11 6 0 multiplying by
 Carried numbers 1 3 8 1 8 TENS
 from multiplication
 by tens go above
 digits

 Carried numbers from adding
 the answers together go
 above the line
Parent and Pupil Numeracy Booklet
 https://corbettmaths.com/2013/06/06/multiplicati
 on-by-10-100-and-1000-2/
Multiplication by 10, 100 and 1000

When multiplying numbers by 10, 100 and 1000 the digits move to left, we do not move the
decimal point.

 Multiplying by 10 - Move every digit one place to the left
 Multiplying by 100 - Move every digit two places to the left
 Multiplying by 1000 - Move every digit three places to the left

 Example 1 46  10 = 460 A zero is used to
 Th H T U
 fill the gap in the
 4 6
 4 6 0 units column

 Example 2 23  100 = 2 300
 Th H T U Zeroes are used to
 2 3 fill gaps in the units
 2 3 0 0 and tens columns

 Example 3 This rule also works for decimals

 345  10 = 345
 Th H T U  101 1
 100

 3  4 5
 3 4  5

The rule of simply adding zeros for multiplication by 10, 100 and 1000 can
be confusing as it does not work for decimals and should therefore be
avoided.

We can multiply by multiples of 10, 100 and 1000 using the same rules as above:

 Example 4 Find 34 x 20 (multiply by 2 then by 10)

 34 x 2 = 68
 68  10 = 680
 68 x 10 = 680 Th H T U
 6 8
 6 8 0
Parent and Pupil Numeracy Booklet
 https://corbettmaths.com/2013/05/19/division-by-
 10-100-and-1000/
Division

Division by 10, 100 and 1000

When dividing numbers by 10, 100 and 1000 the digits move to right, we do not
move the decimal point.

 Dividing by 10 - Move every digit one place to the right
 Dividing by 100 - Move every digit two places to the right
 Dividing by 1000 - Move every digit three places to the right

 Example 1 260  10 = 26
 H T U  1
 10
 1
 100

 2 6 0  Zeros are not generally
 needed in empty columns
 2 6  after the decimal point
 except in cases where a
 specified degree of
 Example 2 439  100 = 439 accuracy is required
 H T U  101 1
 100

 4 3 9 
 4  3 9

 Example 3 This rule also works for decimals

 32·9  10 = 329
 H T U  101 1
 100

 3 2  9
 3  2 9

 We can divide decimals by multiples of 10, 100 and 1000 using the same
 rules as discussed above.

 Example 4 Find 48·6 ÷ 20
 24·3  10 = 2·43
 48·6 ÷ 2 = 24·3 H T U  101 1
 100
 24·3 ÷ 10 = 2·43 2 4  3
 2  4 3
Parent and Pupil Numeracy Booklet
 https://corbettmaths.com/2013/12/28/division-
 video-98/
Division by a single digit
Division can be considered as the reverse process of multiplication.

For example, 2 × 3 = 6 so 6 ÷ 2 ÷ 3 and 6 ÷ 3 ÷ 2 .

Essentially division tells us how many times one number (the divisor) goes into
another (the dividend). From above, 2 goes into 6 three times and 3 goes into 6
two times. The answer from a division is called the quotient. For more difficult
divisions we use the division sign:
 quotient
 divisor dividend

We start from the left of the dividend and calculate how many times the divisor
divides it. This number is written above the division sign. If the divisor does not
divide the digit exactly then the number left over is called the remainder. If
there is a remainder then it is carried over to the next column and the process is
repeated. If there is no remainder then we move directly on to the nextcolumn.

At the end of the dividend if there is still a remainder then in the early stages
pupils are expected to write the remainder after the quotient, however, as a pupil
progresses we expect the dividend to be written as a decimal and the remainder
to be carried into the next column. It is important that digits are lined up
carefully.

Examples
Parent and Pupil Numeracy Booklet

Worked example 1
 810  6

 Estimate
 800  5 = 160

 1 3 5
 2 3
 6 8 1 0

 Example 2 When dividing a decimal by a whole number the
 decimal points must stay in line.
 Carry out a normal
 division

 Example 3 If you have a remainder at the end of a calculation,
 add “trailing zeros” at the end of the decimal and keep
 going!

 Calculate 2·2 ÷ 8 0275
 8 2 2 2 6 0 4 0
 “Trailing Zeros”
Parent and Pupil Numeracy Booklet

Division by a Decimal

When dividing by a decimal we use multiplication by 10, 100, 1000 etc to ensure
that the number we are dividing by becomes a whole number.

 Example 1 24 ÷ 0.3 (Multiply both numbers by 10)

 = 240 ÷ 3
 = 80

 Example 2 4·268 ÷ 0·2 (Multiply both numbers by 10)

 = 42·68 ÷ 2 21 34
 = 21·34 2 42  68

 Example 3 3·6 ÷ 0·04 (Multiply both numbers by 100)

 = 360 ÷ 4
 = 90

 Example 4 52·5 ÷ 0·005 (Multiply both numbers by 1000)

 = 52 500 ÷ 5
 = 10 500

 https://corbettmaths.com/2013/02/15/division-by-
 decimals/

 https://corbettmaths.com/2013/02/15/multiplying-
 decimals-2/
Parent and Pupil Numeracy Booklet

Rounding
Numbers can be rounded to give an approximation.

The rules for rounding are as follows:

 • less than 5 ROUND DOWN
 • 5 or more ROUND UP

 Example 1 Round the following to the nearest ten:

 a) 34 b) 68 c) 283

 Draw a dotted The number beside the one you are
 line after the rounding to helps you decide whether to
 number you are round Up or DOWN
 rounding to

 More than5 –
 ROUND UP

 Example 2 Round the following to the nearest hundred

 a) 267 b) 654 c) 2 393
Parent and Pupil Numeracy Booklet https://corbettmaths.com/2013/09/07/rounding-
 to-1-or-2-decimal-places/

Rounding Decimals
When rounding decimals to a specified decimal place we use the same
rounding rules as before.

 Example 1 Round the following to 1 decimal place:

 a) 4·71 b) 23·29 c) 6·526

 Draw a dotted
 line after the
 decimal place
 being rounded to

 The number in the next decimal
 place helps you to decide whether
 to round up or down

 Example 2 Round the following to 2 decimal places:

 a) 5·673 b) 41·187 c) 5·999

 https://corbettmaths.com/2013/09/07/rounding-
 significant-figures/
Parent and Pupil Numeracy Booklet

Order of Operations
Care has to be taken when performing calculations involving more
than one operation

Consider this: What is the answer to 2 + 4 x 5 ?

Is it (2+4) x 5 or 2 + (4 x 5)
 = 6x5 = 2 + 20
 = 30 = 22

The correct answer is 22.

Calculations should be performed in a particular order following the rules shown
below:

Most scientific calculators follow these rules however some basic calculators
may not. It is therefore important to be careful when using them.

 Example 1 6+5x7 BODMAS tells us to multiply first
 = 6 + 35
 = 41

 Example 2 (6 + 5) x 7 BODMAS tells us to work out the
 = 11 x 7 brackets first
 = 77
 Example 3 3 + 4² ÷ 8 Order first (power)
 = 3 + 16 ÷ 8 Divide
 = 3+2 Add
 = 5
Parent and Pupil Numeracy Booklet

 Example 4 2x4–3x4 BODMAS tells us to multiply first
 = 8 – 12
 =-4

It is important to note that division and multiplication are interchangeable and
so are addition and subtraction. This is particularly important for examples such
as the following:

 Example 5 10 – 3 + 4 In examples like this, go with the
 = 11 order of the question
 i.e. subtract 3 from 10 then add 4
Parent and Pupil Numeracy Booklet https://corbettmaths.com/2013/06/08/negatives-
 addition-and-subtraction-2/

Integers
Despite common misconceptions in young children, the first number is not zero!
The set of numbers known as integers comprises positive and negative whole numbers and the number
zero. Negative numbers are below zero and are written with a negative sign, “ – ”.
Integers can be represented using a number line

Integers are used in a number of real life situations including temperature, profit and loss, height
below sea level and golf scores

Adding and Subtracting integers
Consider 2 + 3.
Using a number line this addition would be “start at 2 and move right 3 places”.

Whereas 2 – 3 would be “start at 2 and move left 3 places”.

Picturing a number line may help pupils extend their addition and subtraction to
integers.

Examples
Addition
 1. 3 + 5 start at 3 and move right 5 spaces, therefore 3 + 5 = 8

 2. – 4 + 7 start at -4 and move right 7 places, therefore – 4 + 7 = 3

Now consider 6 + (-8).

Here we “start at 6 and prepare to move right but then change direction to move
left 8 places because of the (-8). Therefore, 6 + (−8) = −2 and we could rewrite
this calculation as

3. 6 + (−8)
 =6–8
 = −2
Parent and Pupil Numeracy Booklet

Subtraction

 1. 6 − 2 Start at 6 and move left 2 spaces, therefore 6 − 2 = 4

 2. −7 − 4 Start at -7 and move left 4 spaces, therefore −7 − 4 = −11

Similarly, 3 – (-5) can be read as “start at 3 and prepare to move left but
instead change direction because of the (-5) and move right 5 places”.
So 3 – (-5) = 8 and we can write our calculation as

 3. 3 – (−5)
 =3+5
 =8

Method 2: Integer Tiles

A positive tile is worth positive 1 and a negative tile is worth negative 1.
Therefore, when you add one positive tile and one negative tile you get zero.
We call this a ‘zero pair'.

Adding Integers

 1. 2.

3
Parent and Pupil Numeracy Booklet

Subtracting Integers

 1.

 2.

 3.
Parent and Pupil Numeracy Booklet

 https://corbettmaths.com/2012/08/20/multiplying-
 negative-numbers/
Multiplying and dividing Integers

Method 1: Integer tiles https://corbettmaths.com/2012/08/20/dividing-
 involving-negatives/

Multiplying

 1. 2×3

 2. 2 × −3

 3. −2 × −3

 =6

Dividing

 1. 6 ÷ 2 = 3
Parent and Pupil Numeracy Booklet

 2. −6 ÷ 2 = −3

 3. −6 ÷ −2 = 3
How many groups of the second number can be made from the first number?
This question is different since we cannot split something up into negative groups.
Therefore we say to ourselves, how many groups of negative 2 can you make from negative 6?
This will give you your answer of 3.

Once pupils are comfortable with the above methods they will begin to realise for themselves the
following:
Parent and Pupil Numeracy Booklet

Example 1
 a) 5 × 6 = 30 b) −5 × 6 = −30 c) 5 × −6 = −30 d) −5 × −6 = 30

Example 2
 a) 10 ÷ 5 = 2 b) 10 ÷ −5 = −2 c) −10 ÷ 5 = −2 d) −10 ÷ −5 = 2

Example 3
 a) (−6)2 = −6 × −6 = 36

 b) −62 = −(6 × 6) = −36
Parent and Pupil Numeracy Booklet

Fractions

A fraction tells us how much of a quantity we have.
Every fraction has two parts

This is the fraction two fifths which represents two out of five

 1. What fraction of the shape is shaded?

 9
There are 9 parts shaded out of 18 so the fraction is which can
 18
 1
also be simplified to
 2

Equivalent Fractions
When creating and working with equivalent fractions, all S1 pupils will
be issued with a copy of the fraction wall shown below

 23
Parent and Pupil Numeracy Booklet

Equivalent fractions are fractions which have the same value.
To find equivalent fractions we multiply or divide both the numerator
and the denominator of the fraction by the same number.
If you look at the fraction wall you can easily see the equivalent
fractions

 1.

 2.

 3.

 4.

 https://corbettmaths.com/2013/02/15/equivalent-
 fractions/

 24
Parent and Pupil Numeracy Booklet
 https://corbettmaths.com/2013/03/03/simplifying-
 fractions-2/
Simplifying Fractions
To simplify fractions we divide both the numerator and the denominator of the fraction by
the same number. (Ideally this is the highest common factor, HCF, of the numbers, i.e. the
highest number which can divide each number with no remainder.)
We always aim to write fractions in the simplest possible form.

To simplify a fraction, divide the numerator and denominator by the same number.

 Example 1 Example 2

 In examples with higher numbers it is acceptable to use this process
 repeatedly in order to simplify fully.

 Example 3

 https://corbettmaths.com/2012/08/20/fractions-
Fraction of a quantity of-amounts/

Throughout fraction and percentages topics the word “of” represents a multiplication

To find a fraction of a quantity you divide by the denominator and multiply by the numerator.
If it is possible to simplify the fraction first by finding an equivalent fraction then this will make the
calculation easier.

 1.

 25
Parent and Pupil Numeracy Booklet

 2.

Mixed Numbers and Improper Fractions https://corbettmaths.com/2013/02/15/mixed-
 numbers-to-improper-fractions/

If the numerator of a fraction is smaller than the denominator then the fraction is called a proper
fraction.

If the numerator is larger than the denominator then the fraction is an improper fraction.

If a number comprises a whole number and a fraction then it is called a mixed number.

Examples

 26
Parent and Pupil Numeracy Booklet

 3.

 https://corbettmaths.com/2013/02/15/improper-
Improper Fractions to Mixed Numbers fractions-to-mixed-numbers/

To write an improper fraction as a mixed number we calculate how many whole numbers there are (by
considering multiples of the denominator) and then the remaining fraction part

 1.

 27
Parent and Pupil Numeracy Booklet

 2.

 3.

 https://corbettmaths.com/2012/08/21/fractions-
Adding and Subtracting Fractions addition-and-subtraction/

When adding or subtracting fractions it is necessary to have a “common
denominator”

 e.g.

If this is the case then the numerators (top numbers) are simply added or
subtracted.

 28
Parent and Pupil Numeracy Booklet

When fractions have different denominators, equivalent fractions are used to
obtain common denominators.

 Example 1

 Sometimes it is possible to
 turn one of the denominators
 into the other.
 In this case 8 is the lowest
 common denominator

 Example 2 We need to find the lowest
 common multiple of 2 and 3
 in order to find the common
 denominator. In this case,
 the lowest common
 3 denominator is 6.
 2

When adding and subtracting mixed fractions, the fractions are changed to
improper (“top heavy”) fractions first

Example 3

 29
Parent and Pupil Numeracy Booklet
 https://corbettmaths.com/2012/08/21/multiplying-
 fractions-2/
Multiplying and Dividing Fractions
To multiply fractions simply multiply the numerators together and the denominators
together then simplify.

 2 1 Fractions can be
Example 1:  simplified prior to
 3 5 multiplying to keep
 2 1 the numbers as
 =
 3 5 small as possible
 2
 =
 15

 Find one numerator and one
 denominator that are
 divisible by the same
 number – this is called
 “cancelling”

Example 2: 2 × 
 
 As with adding and
 =
 
 ×
 
 subtracting fractions,
 
 when multiplying mixed
 × 
 = fractions they should be
 × 
 turned into improper
 = 
 fractions first.

 = 

 https://corbettmaths.com/2012/08/21/division-with-
Dividing fractions
 fractions/

A deep understanding of dividing fractions will be given in class using concrete an pictorial approaches.
Once understood the following quick method can be used

 1. Flip the fraction you are
 dividing by upside down
 2. Multiply the fractions
 together
 3. Simplify where possible

 30
Parent and Pupil Numeracy Booklet

Example 1: Example 2: 
 ÷ ÷ 
 
 × 
 ÷ 

 × 
 ×
 × 

 = =
 
 31
Parent and Pupil Numeracy Booklet

 https://corbettmaths.com/2013/02/15/fdp/
Percentages
Percent means “per hundred”, i.e. out of 100.

A percentage can be converted to an equivalent fraction or decimal
by dividing by 100.
 24 12 6
 Fraction: 24% = 100 = 50 = 25
 1. Write 24% as a fraction and a decimal
 24
 Decimal: is 24 ÷ 100 = 0.24
 100

 72 36 18
 2. Write 72% as a fraction and a decimal Fraction: 72% = 100 = 50 = 25

 72
 Decimal: is 72 ÷ 100 = 0.72
 100

 The following diagram is an easy way to remember FDP equivalence

 32
Parent and Pupil Numeracy Booklet

Common Percentages
It is recommended that the information in the table below is learned. The
decimal and fraction equivalents of common percentages are used in percentage
calculations.

 Percentage Fraction Decimal
 1
 1% 0·01
 100
 1
 5% 0·05
 20
 1
 10% 0 ·1
 10
 1
 20% 0 ·2
 5
 1
 25% 0·25
 4
 1 1
 33 % 0·3333…
 3 3
 1
 50% 0 ·5
 2
 2 2
 66 % 0·66666…
 3 3
 3
 75% 0·75
 4
 100% 1 1

Finding percentages of an amount using equivalent fractions (Non-Calculator)

When calculating common percentages of a quantity, the fractional equivalents can be useful

 1. Find 25% of £240 2. Find 20% of £180

 1 1
 25% = 20% =
 4 5

 1 1
 £240 £180
 4 5

 = £240 ÷ 4 = £180 ÷ 5

 = £80 = £36

 33
Parent and Pupil Numeracy Booklet

Finding 10%

Using the same method from ‘Fraction of a quantity’ we know that when finding one tenth of a given
value we divide by 10

 1. Find 10% of 50 2. Find 10% of 73

 10% 50 10% 73

 = 50 ÷ 10 = 73 ÷ 10

 =5 = 7.3

We can also use this method to find multiples of 10%

 3. Find 20% of 80 4. Find 70% of 450

 10% 80 = 80 ÷ 10 10% 450 = 450 ÷ 10
 =8 = 45

 20% 80 = 8 × 2 70% 450 = 45 × 7
 = 16 = 315

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Parent and Pupil Numeracy Booklet

Finding 5%

To calculate 5% of a given quantity, first find 10% and then divide your answer by 2 (10% ÷ 2 = 5%)

 1. Find 5% of 60 2. Find 5% of 84

 10% 60 10% 84

 = 60 ÷ 10 = 84 ÷ 10

 =6 = 8.4

 5% 60 = 6 ÷ 2 5% 84 = 8.4÷ 2
 =3 = 4.2

Finding 1% and multiples of 1%

When we want to calculate 1% of a given quantity we divide by 100.

When dividing by 100 the digits move to the right by 2 places

 1. Find 1% of 4000 2. Find 1% of 375

 1% 4000 1% 375

 = 4000 ÷ 100 = 375 ÷ 100

 = 40 = 3.75

We can also use this method to find multiples of 1%

 3. Find 3% of 750 4. Find 7% of 65

 1% 750 = 750 ÷ 100 1% 65 = 65 ÷ 100
 = 7.5 = 0.65

 3% 750 = 7.5 × 3 7% 65 = 0.65 × 7
 = 22.5 = 4.55

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Parent and Pupil Numeracy Booklet
 https://corbettmaths.com/2012/08/20/percentages
 -of-amounts-non-calculator/
Finding any percentage of a given value

We can now use the above skills to calculate any percentage of a given quantity

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Parent and Pupil Numeracy Booklet

Percentages on a Calculator

To find a percentage of a quantity using a calculator, divide the
percentage by 100 and multiply by the amount.

 1. Find 7% of 150

 7
 × 150
 100

 =7 ÷ 100 × 150
 =10.5

 2. Find 81% of £35

 81
 × 35
 100

 =81 ÷ 100 × 35

 =£28.35

 3. Find 23% of £15 000

 23
 × £15000
 100

 =23 ÷ 100 × 150000

 =£3450

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Parent and Pupil Numeracy Booklet

Expressing One Quantity as a Percentage of Another

 You can express one quantity as a percentage of another as follows:

 - Make a fraction
 - Divide the numerator by the denominator
 - Multiply by 100

 Example 1 Ross scored 45 out of 60 in his Maths test. What is his
 percentage mark?

 45
 45 ÷ 60 x 100 = 75%
 60

 Example 2 There are 30 pupils in 1A2. 18 are girls.
 What percentage of the pupils are girls?

 18
 18 ÷ 30 x 100 = 60%
 30

 Example 3 A survey of pupils’ favourite sports was taken and the
 results were as follows:

 Football – 11 Rugby – 3 Tennis – 4 Badminton – 2

 What percentage of pupils chose tennis as their favourite
 sport?

 Total number of pupils = 11 + 3 + 4 + 2 = 20
 4 out of 20 pupils chose tennis

 4
 So, 4 ÷ 20 x 100 = 20%
 20

 20% of pupils chose tennis as their favourite subject.

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Parent and Pupil Numeracy Booklet
 https://corbettmaths.com/2013/02/15/reverse-
 percentages/
Reverse the change
To help us find the original value of something after a percentage increase or
decrease we use a bar model.
The original value of something is always going to be 100%.

 1. I bought a jacket for £81 in the sale. It had 10% off.
 How much did it originally cost?

 The original value has decreased, so we subtract this from 100%.
 What % did I get it for? 100% − 10% = 90%

 We have shown that each 10% is worth 9
 Therefore, original price is 10 × 9 = £90

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Parent and Pupil Numeracy Booklet

 2. The gas company has increased their monthly charges by 20%. The average gas bill is now £96
 per month. How much was the original average gas bill?

 The original value has increased, so we add this to 100%.

 40
Parent and Pupil Numeracy Booklet

Ratio
A ratio is a way of comparing amounts of something.
The ratio can be used to calculate the amount of each quantity or to share a
total into parts.

Writing Ratios

The order is important when writing ratios.

 1. For the diagram shown write down the ratio of

 a) footballs : tennis balls
 b) hockey pucks : basketballs

 footballs : tennis balls hockey pucks : basketballs
 = 3 : 4 = 1 : 7

 2. In a baker shop there are 122 loaves, 169 rolls and 59 baguettes.

 The ratio of loaves : baguettes : rolls is

 122 : 59 : 169

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Parent and Pupil Numeracy Booklet

 https://corbettmaths.com/2013/03/03/simplifying-
Simplifying Ratios ratio/

Ratios can be simplified in much the same way as fractions by dividing all of the
parts of the ratio by the same number

 e.g. 12 : 6 : 3 can be simplified by dividing by 3 to get 4 : 2 : 1

 https://corbettmaths.com/2013/03/03/ratio-
Using Ratios sharing-the-total/

A given ratio can be used to find quantities by scaling up or down.

 Example The ratio of boys to girls at a party is 2 : 3.
 If there are 16 boys at the party, how many girls are
 there?

 Put the ratio at the
 top

 Find how the given value has been
 scaled up/down and do the same So there are 24 girls at the
 to the other side party.

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Parent and Pupil Numeracy Booklet

 https://corbettmaths.com/2013/05/16/ratio-given-
Sharing in a Given Ratio one-quantity/

Example Chris, Leigh and Clare win £900 in a competition.
 They share their winnings in the ratio 2 : 3 : 4. How much
 does each person receive?

 1. Find the total number of shares

 2+3+4=9 i.e. there are 9 shares

 2. Divide the amount by this number to find the value of each share

 £900 ÷ 9 = £100 i.e. each share is worth £100

 3. Multiply each figure in the ratio by the value of each share 2

 shares: 2 x £100 = £200
 3 shares: 3 x £100 = £300
 4 shares: 4 x £100 = £400
 4. Check that the total is correct by adding the values together

 £200 + £300 + £400 = £900

 So Chris receives £200, Leigh receives £300 and Clare receives £400.

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Parent and Pupil Numeracy Booklet

 https://corbettmaths.com/2013/04/04/direct-
Direct Proportion proportion/

Two quantities are said to be in direct proportion if when one quantity increases
the other increases in the same way e.g. if one quantity doubles the other doubles.

When solving problems involving direct proportion the first calculation is to find
one of the quantities.

Example 1 5 fish suppers costs £32.50, find the cost of 7 fish suppers.

 The first calculation
 is always a divide

 Find the cost
 of one
 So 7 fish suppers would cost £45.50.

 Example 2 5 adult tickets for the cinema cost £27.50. How much would
 8 tickets cost?

 The cost of 8 adult tickets is £44

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Parent and Pupil Numeracy Booklet

 https://corbettmaths.com/2013/04/04/inverse-
Inverse Proportion proportion/

Two quantities are said to be in inverse proportion if when one quantity increases
the other decreases e.g. when one quantity doubles the other halves.

When solving problems involving inverse proportion the first calculation is to find
one of the quantities.

 Example 1 If 3 men take 8 hours to build a wall, how long would it
 take 4 men to build the same wall?
 (Common sense should tell us that it will take less time
 as there are more men working)

 The first calculation is
 One man would always a multiply
 take 24 hours

 4 men would take 6 hours to build the wall.

 Example 2 An aeroplane takes 5 hours for a journey at an
 average speed of 500km/h.
 At what speed would the aeroplane have to travel to
 cover the same journey in 4 hours?

 Common sense –
 Find speed less time so
 for 1 hour more speed
 required!

 The aeroplane would need to fly at an average speed of 625km/h

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Parent and Pupil Numeracy Booklet

Time
12 hour Clock

Time can be displayed on a clock face or a digital clock.

When writing times in 12 hour clock we need to add a.m. or p.m. after the time.

 a.m. is used for times between midnight and 12 noon (morning)
 p.m. is used for times between 12 noon and midnight (afternoon/evening)

 NOTE: 12 noon 12.00 p.m.
 12 midnight 12.00 a.m.

24 hour Clock

When writing times in 24 hour clock a.m. and p.m. should not be used
Instead, four digits are used to write times in 24 hour clock.

After 12 noon, the hours are numbered 13:00, 14:00, . . . to represent 1p.m, 2p.m respectively

 Examples

 6:30 a.m. 06:30

 12:00 p.m. 12:00

 2:45 p.m. 14:25

 8:25 p.m. 20:25

 12:00 a.m. 00:00

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Parent and Pupil Numeracy Booklet

Time Intervals https://corbettmaths.com/2013/10/24/calculations-
 involving-time/

We do not teach time as a subtraction, instead we “count on”.

Example 1

How long is it from 8.40am to 1.25pm?
 start next correct correct
 time o’clock hour minutes

8.40am 9.00am 1.00pm 1.25pm
 20 mins 4 hours 25 mins

 = 4 hours 45 minutes

Example 2

How long is it from 0935 to 1645?

start next correct correct
time o’clock hour minutes

0935 1000 1600 1645
 25 mins 6 hours 45 mins

 = 6 hours 70 minutes
 = 6 hours + (1 hour 10 minutes)
 = 7 hours 10 minutes

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Parent and Pupil Numeracy Booklet

Converting from minutes to hours

To convert from minutes to hours we write the minutes as a fraction of an hour (i.e. 60
minutes; so 60 is the denominator).

Example 1 Write 48 minutes in hours.

 48
 60
 = 48 ÷ 60
 = 0·8 hours

Example 2 Write 3 hours and 36 minutes in hours.

 36
 3+
 60
 = 3 + (36 ÷ 60)
 = 3 + 0·6
 = 3·6 hours

Converting from hours to minutes

To convert from hours to minutes we multiply the decimal minutes by 60.

Example 1 Write 0∙3 hours in minutes.

 0·3 × 60
 = 18 minutes

Example 2 Write 5∙65 hours in hours and minutes.

 5 hours + (0·65 × 60) min utes
 = 5 hours 39 min utes

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Parent and Pupil Numeracy Booklet

 https://corbettmaths.com/2016/01/01/speed-
 distance-time/

Distance, Speed and Time

The use of a triangle when calculating distance, speed and time will be
familiar to pupils.

Example 1 A car travels at an average speed of 40mph for 5 hours.
 Calculate the distance covered.

 S = 40 mph T = 5 hours

 D=SxT
 = 40 x 5
 = 200 miles

Example 2 Calculate the average speed of a car which travels a distance
 of 168 miles in 3 hours and 30 mins.

 D = 168 miles T = 3 hours 30 mins = 3·5 hours

 S=D÷T
 Time should be written as a
 = 168 ÷ 3·5
 decimal in SDT calculations
 = 48 mph

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Parent and Pupil Numeracy Booklet

Example 3 Calculate the time taken for a car to travel a distance of 84 miles at
 an average speed of 35 mph.

 D = 84 miles S = 35 mph
 Change decimal time to
 hours and minutes by
 T=D÷S multiplying the decimal by
 = 84 ÷ 35 60 i.e. 0·4 x 60 = 24
 = 2·4 hours (= 2 hours 24 mins)

 50
Parent and Pupil Numeracy Booklet

Information Handling – Bar Graphs and
Histograms

Bar graphs and histograms are often used to display information. The horizontal
axis should show the categories or class intervals and the vertical axis should
show the frequency.

All graphs should have a title and each axis must be labelled.

Example 1 The histogram below shows the height of P7 pupils

 Height of P7 pupils

 8
 7
 Number of pupils

 6
 5
 4
 3
 2
 1
 0
 130-134 135-139 140-144 145-149 150-154 155-159 160-164 165-169

 Height (cm)

Note that the histogram has no gaps between the bars as the data is
continuous i.e. the scale has meaning at all values in between the ranges given.
The intervals used must be evenly spaced (it must remain in this order).

 Example 2 The bar graph below shows the results of a survey on
 favourite sports.

 https://corbettmaths.com/2012/08/10/readin
 g-bar-charts/
 51
Parent and Pupil Numeracy Booklet

Note that the bar graph has gaps between the bars. The information displayed is
non-numerical and discrete i.e there is no meaning between values (e.g. there is no
in between for tennis and football). This means the order of the bars can be
changed.

 Examples of discrete data:

 • Shoe Size
 • Types of Pet
 • Favourite subjects
 • Method of travel to school

 Examples of continuous data:

 • Heights of pupils
 • Weights
 • Lengths of journeys to work
 • Marks in a test
 https://corbettmaths.com/2013/05/12/discret
 e-and-continuous-data-corbettmaths/

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Parent and Pupil Numeracy Booklet

 https://corbettmaths.com/2013/05/22/line-graphs/
Information Handling – Line Graphs

Line graphs consist of a series of points which are plotted, then joined by a line.
All graphs should have a title and each axis must be labelled. Numbers are written
on a line and the scales are equally spaced and consistent. The trend of a graph is
a general description of it.

 Example 1

 A comparative line graph can
 be used to compare data
 Example 2 sets. Each line should be
 labelled or a key included.

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Parent and Pupil Numeracy Booklet
 https://corbettmaths.com/2012/08/10/scatter-
 graphs/

Information Handling – Scatter Graphs

A scatter graph allows you to compare two quantities (or variables). Each variable
is plotted along an axis.
A scatter graph has a vertical and horizontal axis and requires a title and
appropriate x and y - axis labels.
For each piece of data a point is plotted on the diagram and the points are not
joined up.

A scatter graph allows you to see if there is a connection (correlation) between
the two quantities. There may be a positive correlation when the two quantities
increase together e.g. sale of umbrellas and rainfall. There may be a negative
correlation where as one quantity increases the other decreases e.g. price of a car
and the age of the car. There may be no correlation e.g. distance pupils travel to
school and pupils’ heights.

 Example The table shows the marks gained by pupils in Maths and
 Science Tests. This information has been plotted on a
 scatter graph.

 Maths Score 5 6 10 11 14 15 18 23
 Science Score 7 10 11 15 18 17 19 25

 A comparison of pupils' Maths and
 Science marks
 Science mark (out of 25)

 25
 20
 15
 10
 5
 0
 0 5 10 15 20 25
 Maths mark (out of 25)
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Parent and Pupil Numeracy Booklet

 https://corbettmaths.com/2013/05/25/interpreting

Information Handling – Pie Charts -pie-charts

A pie chart can be used to display information.
Each sector of the pie chart represents a different category.

The size of each category can be worked out as a fraction of the total using the
number of divisions or by measuring angles.

Using Fractions

 Example 30 pupils were asked the colour of their eyes.
 The results are shown in the pie chart below.

 How many pupils had brown eyes?

 The pie chart is divided up into ten equal parts, so pupils
 2
 with brown eyes represent of the total.
 10

 2
 of 30 = 6 (30 ÷ 10 x 2) so 6 pupils had brown eyes
 10

 Using Angles

 If no divisions are marked on the pie chart and we are given the angles
 instead we can still work out the fraction by using the angle of each
 sector.

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Parent and Pupil Numeracy Booklet

 The angle of the brown sector is 72°. We can calculate the number of
 pupils as follows:

 angle
  total
 360
 i.e. the number of pupils with brown eyes is

 72
  30 = 6
 360

 NB: Once you have found all of the values you can check your
 answers by making sure the total is 30.

 https://corbettmaths.com/2013/02/27/drawing-a-
 Drawing Pie Charts pie-chart/

 On a pie chart, the size of the angle for each sector is calculated as a
 fraction of 360°.

 We calculate the angles as follows:

 amount
  360
 total

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Parent and Pupil Numeracy Booklet

Example In a survey about television programmes, a group of people were asked
what their favourite soap was. Their answers are given in the table below. Draw a
pie chart to illustrate this information.

 Soap Number of people
 Eastenders 28
 Coronation Street 24
 Emmerdale 10
 Hollyoaks 12
 None 6

 Step 1: Calculate the total number of people.

 Total = 28 + 24 + 10 + 12 + 6 = 80

 Step 2: Calculate the angles using the formula:

 amount
  360
 total

 28
 Eastenders:  360 = 126
 80
 24
 Coronation Street:  360 = 108
 80
 10
 Emmerdale:  360 = 45
 80
 12
  360 = 54
 Hollyoaks:
 80
 6
 None:  360 = 27
 80
 Always check that the angles add up to 360°.

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Parent and Pupil Numeracy Booklet

 Step 3: Draw the pie chart
 Completed pie charts
 should be labelled or a key
 drawn to indicate what
 each sector represents.

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Parent and Pupil Numeracy Booklet

Information Handling – Averages
To provide information about a set of data, the average value may be given. There
are 3 ways of finding the average value – the mean, the median and the mode.

 Mean https://corbettmaths.com/2012/08/02/the-mean/

 The mean is found by adding all of the values together and dividing by the
 number of values

 e.g. 7 9 7 5 6 7 12 9 10

 9 values in Mean = (7 + 9 + 7 + 5 + 6 +7 + 12 + 9 + 8) ÷ 9
 the set = 72 ÷ 9
 =8

 Median https://corbettmaths.com/2012/08/02/the-median/

 The median is the middle value when all of the data is written in numerical
 order (smallest to largest).

 e.g. 7 9 7 5 6 7 12 9 10

 Ordered list: 5 6 7 7 7 9 9 10 12

 Median = 7

 NOTE: If there are two values in the middle, the median is the mean of
 those two values.

 e.g. 5 6 7 7 7 9 9 10 12 13

 Median = (7 + 9) ÷ 2
 = 16 ÷ 2
 =8

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Parent and Pupil Numeracy Booklet

 https://corbettmaths.com/2013/12/21/the-mode-
 Mode video56/

 The mode is the value that occurs most often in the data set.

 e.g. 5 6 7 7 7 9 9 10 12

 Mode = 7

 Range https://corbettmaths.com/2012/08/02/the-range-video/

 We can also calculate the range of a data set. This gives us a measure of
 spread.

 e.g. 5 6 7 7 7 9 9 10 12

 Range = highest value – lowest value
 = 12 – 5
 =7

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Parent and Pupil Numeracy Booklet

Evaluating Formulae
To find the value of a variable in a formula, we substitute all of the given values
into the formula and use the BODMAS rules to work out the answer.

 Example 1 Use the formula P = 2L + 2B to evaluate P when L = 12 and
 B=7.

 Step 1: Write the formula P = 2L + 2B
 Step 2: Substitute numbers for letters P = 2 12 + 2  7
 Step 3: Start to evaluate (use BODMAS) P = 24 +14
 Step 4: Write answer P = 38

 V
 Example 2 Use the formula I= to evaluate I when V = 240 and
 R
 R = 40 .

 V Evaluate means find
 I= the value of . . .
 R
 240
 I=
 40
 I=6

 Example 3 Use the formula F = 32 +1 8C to evaluate F when C = 20 .

 F = 32 +1 8C
 F = 32 +18 20
 F = 32 + 36
 F = 68

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Parent and Pupil Numeracy Booklet

 https://corbettmaths.com/2013/12/28/collecting-like-
 terms-video-9/
Collecting Like Terms

An expression is a collective term for numbers, letters and operations

 e.g. 3x + 2y − z 4m2 + 5m −1

An expression does not contain an equals sign.

We can “tidy up” expressions by collecting “like terms”. We circle letters which
are the same (like) and simplify.

 Example 1 Simplify x + y + 3x

 Circle the “like terms” and
 collect them together.

 Don’t forget to circle
 the sign as well!

 Example 2 Simplify 2a + 3b + 6a – 2b
 Use a box for different like
 terms to make it stand out

 Example 3 Simplify 2w² + 3w + + 3w² - w

 Note that w² and w do not
 have the same exponents
 and are therefore not “like
 terms”

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Parent and Pupil Numeracy Booklet

Angles

Types of angles

 obtuse
 acute right

 reflex
 straight

 An acute angle is smaller than 90o.

 A right angle is EXACTLY 90o.

 An obtuse angle is between 90o and 180o.

 A straight line is EXACTLY 180o.

 A reflex angle is between 180o and 360o.

 A full turn is EXACTLY 360o.

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Parent and Pupil Numeracy Booklet

Naming angles

3 capital letters are used when naming an angle. We also use  which is the sign for angle.

 C We would name this angle  ABC or  CBA. The
 lines AB and BC are called the arms of the angle
 and B is called the vertex. This means that the
 A letter B must be in the middle when naming
 B
 the angle, however, it doesn’t matter whether A
 or C is first.

Example 1

  QDP OR  PDQ

Example 2

  PTY OR  YTP

Example 3

  BCA OR  ACB

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Parent and Pupil Numeracy Booklet

Other types of angles

Complementary angles add up to 90o.

Supplementary angles add up to 180o.

Vertically opposite angles are equal.

 Vertically Opposite (X-angle)

Corresponding angles are equal.
(Sometimes referred to as F angles.)

 The arrows on these
 lines show that they
 are parallel
 Corresponding Angles (F-angle)

Alternate angles are equal.
(Sometimes referred to as Z angles.)

 Alternate Angles (Z-angle)

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Parent and Pupil Numeracy Booklet

Coordinates

 A coordinate point describes the location of
 a point with respect to an origin.
 A Cartesian diagram consists of a horizontal
 axis (x - axis) and a vertical axis (y - axis).
 Where the two axes meet is the origin.

Important Points

 • A ruler should be used to draw the axes and they should be clearly labelled. (the
 numbers go ON the line, not in the box)

 • For a coordinate point the first number describes how far along the x-axis the point is
 and the second refers to how far it is up or down the y-axis. (along then up)

 • Coordinate points are enclosed in round brackets and the two numbers are separated by
 a comma i.e. (2, -3)

 • If a letter appears before a coordinate point then we can label the point once it has
 been plotted i.e. D(-2, 4)

 • The origin is the point (0, 0) – this is where the x and y axes cross over

 • Positive numbers are to the right of the origin on the x-axis and above the origin on the
 y-axis.

 • Negative numbers are to the left of the origin on the x-axis and below the origin on the
 y-axis.

 • Numerical values should refer to a line – not a box.

 • Each axis must have equal spacing from one number to the next.

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Parent and Pupil Numeracy Booklet

Example Plot the coordinate points A(2, 3), B(-3, 2), C(-2, -4) and D(4, -2).

 y
 Along 2
 and up 3
 4
 A
 3
 Along -3 B
 2
 and up 2
 1

 -4 -3 -2 -1 0 1 2 3 4 x
 -1
 D
 -2
 Along 4 and
 -3 down 2
 C
 -4

 Along -2 and down 4

ALWAYS x before y, just like the alphabet!

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Parent and Pupil Numeracy Booklet

Measurement

Pupils should be able to work with a range of different units of measurements relating to
length, weight, volume etc.

Pupils should be able to identify a suitable unit for measuring certain objects, i.e.

 Fingernail: millimetres (mm)

 Desk: centimetres (cm)

 Football Pitch: metres (m)

 Distance from Glasgow to Edinburgh: kilometres (km)

In Home Economics, learners will work with a wide range of measurements when dealing with
quantities of food or liquids.

 Grams (g) and kilograms (kg) are used to
 weigh cooking ingredients.

 Measuring jugs allow liquids to be
 measured in millilitres (ml) and
 litres (l).

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Parent and Pupil Numeracy Booklet

In the Technical department, measurements are generally in millimetres (mm).

 There are 10 mm in 1 cm, often
 rulers are marked in centimetres with
 small divisions showing the millimetres.

In Mathematics pupils look at converting between all of these different units. Here are some
useful conversions to note:

 LENGTH WEIGHT

 10 millimetres = 1 centimetre 1000 grams = 1 kilogram

 100 centimetres = 1 metre 1000 kilograms = 1 tonne

 1000 metres = 1 kilometre

 VOLUME

 1cm3 = 1 millilitre

 1000 millilitres = 1 litre

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Parent and Pupil Numeracy Booklet

 Additional Useful websites

There are many valuable online sites that can offer help and more practice. Many
are presented in a games format to make it more enjoyable for your child.

The following sites may be found useful:

 www.mymaths.co.uk

 (holyrood2, angles291)

 www.mathsbot.com

 www.corbettmaths.com

 www.amathsdictionaryforkids.com

 www.woodland-juniorschool.kent.sch.uk

 www.bbc.co.uk/schools/bitesize

 www.topmarks.co.uk

 www.primaryresources.co.uk/maths

 www.mathsisfun.com

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